Problem: Jessica is 12 years older than Stephanie. Fifteen years ago, Jessica was 3 times as old as Stephanie. How old is Stephanie now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Stephanie. Let Jessica's current age be $j$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $j = s + 12$ Fifteen years ago, Jessica was $j - 15$ years old, and Stephanie was $s - 15$ years old. The information in the second sentence can be expressed in the following equation: $j - 15 = 3(s - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = s + 12$ . Substituting this into our second equation, we get the equation: $(s + 12)$ $-$ $15 = 3(s - 15)$ which combines the information about $s$ from both of our original equations. Simplifying both sides of this equation, we get: $s - 3 = 3 s - 45$ Solving for $s$ , we get: $2 s = 42$ $s = 21$.